Estimation of actual proportion of loanwords in a language. (English) Zbl 1377.62048
Summary: We suggest a modification of probability proportional to size with replacement (PPSWR) sampling method to estimate the actual proportion of loanwords in a language. When the proposed modification to PPSWR sampling can be implemented, the modification leads to an estimator which performs better than the estimator in a PPSWR sampling design. Under the assumptions that some words have a relatively very high frequency whereas most of the words have low frequency, we show that the estimator under the PPSWR scheme is better than the estimator under the simple random sampling without replacement (SRSWOR). The suggested procedure has been applied to estimate the usage-based (actual) proportion of the Persian and Arabic loanwords in contemporary Marathi.
MSC:
| 62D05 | Sampling theory, sample surveys |
| 62P99 | Applications of statistics |
| 68T50 | Natural language processing |
| 91F20 | Linguistics |
Keywords:
confidence interval; Marathi; Persian-Arabic loanwords; probability proportional to size sampling; simple random sampling without replacement; Zipf’s lawReferences:
| [1] | Cochran, W. G. (1977) Sampling Theory Third Edition. Wiley, New York. |
| [2] | Date, Y.R., Karve, C.G., Chandorkar, A. and Datar, C.S. (1932-1950) Mahārāṣṭra Śabdakośa 7 volumes plus a supplement, Maharashtra Kosamandala Limited, Pune. · Zbl 0343.60012 |
| [3] | Gabaix, X. (1999) Zipf’s Law and the Growth of Cities The American Economic Review 89 Papers and Proceedings of the One Hundred Eleventh Annual Meeting of the American Economic Association. · Zbl 0343.60012 |
| [4] | Hidiroglou, M. A. (1986) The construction of a self-representing stratum of large units in survey designs American Statistician40, 27-31. |
| [5] | Hill, B. M. (1970) Zipf’s Law and Prior Distributions for the Composition of a Population Journal of the American Statistical Association65, 1220-1232. · Zbl 0224.92011 · doi:10.1080/01621459.1970.10481157 |
| [6] | Kulkarni, K. P. (1993) Marāṭhī Vyutpatti Kośa (Marathi Etymological Dictionary) Shubhada Saraswat Prakashan, Third Edition, Pune. |
| [7] | Sukhatme, P. V., Sukhatme, B.V., Sukhatme, S. and Asok, C. (1984) Theory of sample surveys with applications Indian Society for Agricultural Statistics, New Delhi. · Zbl 0344.62010 |
| [8] | Woodroofe, M. and Hill, B. On Zipf’s Law Journal of Applied Probability12, 425-434. · Zbl 0343.60012 · doi:10.1017/S0021900200048233 |
| [9] | Zipf, G.K. (1949). Human Behaviour and the Principles of Least Effort Addison-Wesley. · Zbl 0343.60012 |
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